This proposed study is concerned with an investigation of a group of mathematical models of the eye of the horseshoe crab Limulus, which falls under the heading of the "adapting bump model". The investigations are particularly concerned with a functional relationship satisfied by the real eye and some of the models: the voltage power spectrum is proportional to the square of the modulus of the light-to-voltage transfer function (or flicker response). We propose to attempt to classify those models which behave like the eye in this respect, by analytical techniques where possible, and to develop numerical methods in other cases. In another line of investigation we plan to test the model and answer some open questions with a simulation of the model by Monte Carlo methods and comparison with laboratory data.